SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 248115 10.22130/scma.2021.531698.942 Research Paper An Introduction to Spectral Theory of Bounded Linear Operators in Intuitionistic Fuzzy Pseudo Normed Linear Space An Introduction to Spectral Theory of Bounded Linear Operators in Intuitionistic Fuzzy Pseudo Normed Linear Space Dinda Bivas Department of Mathematics, Mahishamuri Ramkrishna Vidyapith, Howrah 711401, WB, India and Department of Mathematics, Kazi Nazrul University, Asansol 713340, WB, India Ghosh Santanu Kumar Department of Mathematics, Kazi Nazrul University, Asansol 713340, WB, India. Samanta Tapas Kumar Department of Mathematics, Uluberia College, Howrah 711315, WB, India 01 02 2022 19 1 1 13 06 06 2021 15 12 2021 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_248115.html

In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator \$P\$ in an IFPNLS, the resolvent set \$rho(P)\$ and spectrum \$sigma(P)\$ are nonempty, \$rho(P)\$ is open and \$sigma(P)\$ is closed set.

Intuitionistic fuzzy pseudo norm Resolvent Spectrum Strongly intuitionistic fuzzy bounded linear operator Pseudo norm
 K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), pp. 87-96.  T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear space, J. Fuzzy Math., 11 (2003), pp. 687-705.  T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst., 151 (2005), pp. 513-547.  S.C. Cheng and J.N. Mordeson, Fuzzy Linear Operators and Fuzzy Normed Linear Spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429-436.   B. Dinda, S.K. Ghosh and T.K. Samanta, Intuitionistic fuzzy pseudo normed linear spaces, New Math. Nat. Comput., 15 (2019), pp. 113-127.  B. Dinda, S.K. Ghosh and T.K. Samanta, On w-Convergence and s-Convergence in intuitionistic fuzzy pseudo normed linear spaces, New Math. Nat. Comput., 17(3), (2021), pp. 623-632.  B. Dinda, S.K. Ghosh and T.K. Samanta, Relations on continuities and boundedness in intuitionistic fuzzy pseudo normed linear spaces, South East Asian J. of Mathematics and Mathematical Sciences, 17(3), (2021), pp. 15-30.  C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst., 48 (1992), pp. 239-248.  I. Golet, On generalized fuzzy normed spaces and coincidence fixed point theorems, Fuzzy Sets Syst., 161 (2010), pp. 1138-1144.  A.K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets Syst., 6 (1981), pp. 85-95.  A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12 (1984), pp. 143-154.  E. Kreyszig, Introductory functional analysis with applications, John Wiley & Sons, New York-London-Sydney, 1978.   S. Nu adu aban, Fuzzy pseudo-norms and fuzzy F-spaces, Fuzzy Sets Syst., 282 (2016), pp. 99-114.  R. Saadati and J.H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), pp. 331-344.  A. Samee A., A. Jameel K. and F. Ali C., Spectral theory in fuzzy normed spaces, Al-Nahrain Journal of Science, 14(2), (2011), pp. 178-185.  H.H. Schaefer and M.P. Wolff, Topological Vector Spaces, Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.  J.Z. Xiao and X.H. Zhu, On linearly topological structures and property of fuzzy normed linear space, Fuzzy Sets Syst., 125 (2002), pp. 153-161.  L.A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), pp. 338-353.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 248906 10.22130/scma.2021.140147.873 Research Paper A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly \$L\$--Lipschitzian Asymptotically Generalized \$Phi\$-Hemicontractive Mappings A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly \$L\$--Lipschitzian Asymptotical Ofem Austine Efut Department of Mathematics, University of Uyo, Uyo, Nigeria. Igbokwe Donatus Ikechi Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria. 01 02 2022 19 1 15 40 19 11 2020 03 01 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_248906.html

In this paper, we introduce a three-step implicit iteration scheme with errors for finite families of nonexpansive and uniformly \$L\$-Lipschitzian asymptotically generalized \$Phi\$-hemicontractive mappings in real Banach spaces. Our new implicit iterative scheme properly includes several well known iterative schemes in the literature as its special cases. The results presented in this paper extend, generalize and improve well known results in the existing literature.

Fixed point Nonexpasive mapping Uniformly \$L\$--Lipschitzian asymptotically generalized \$Phi\$-Hemicontractive mapping strong convergence Banach spaces Normalized duality mapping
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Chidume and C.O. Chidume, Convergence theorems for fixed points of uniformly continuous    generalized \$Phi\$-hemi-contractive mappings, J. Math. Anal. Appl., 303 (2005), pp. 545-554.  C.E. Chidume and C.O. Chidume, Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators, Proc. Amer. Math. Soc., 134 (2006), pp. 243-251.     R.C. Chen, Y.S. Song and H. Zhou, Convergence theorems for implicit iteration process for a finite family continuous pseudocontractive mappings, J. Math. Anal. Appl., 314 (2006), pp. 701-706.  Y.J. Cho, H.Y. Zhou and G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47 (2004), pp. 707-717.  P. Chuadchawna, A. Farajzadeh and A. Kaewcharoen, On convergence theorems for two generalized nonexpansive multivalued mappings in hyperbolic spaces, Thai J. Math., 17 (2019), pp. 445-461.  P. Chuadchawna, A. Farajzadeh and A. Kaewcharoen, Fixed-point approximations of generalized nonexpansive mappings via generalized M-iteration process in hyperbolic spaces, Int. J. Math. Math. Sci., (2020), pp. 1-8, article ID 6435043.  P. Chuadchawna, A. Farajzadeh and A. Kaewcharoen, Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces, J. Appl. Anal., 27 (2021), pp. 129-142.  G. Das and J.P. Debata, Fixed points of Quasi-nonexpansive mappings, Indian J. Pure. Appl. Math., 17 (1986), pp. 1263-1269.  L.C. Deng, P. Cubiotti and J.C. Yao, Approximation of common fixed points of families of nonexpansive mappings, Tai. J. Math., 12 (2008), pp. 487-500.  L.C. Deng, P. Cubiotti and J.C. Yao, An implicit iteration scheme for monotone variational inequalities and fixed point problems, Nonlinear Anal., 69 (2008), pp. 2445-2457.  L.C. Deng, S. Schaible and J.C. Yao, Implicit iteration scheme with perturbed mapping for equilibrium problems and fixed point problems of finitely many nonexpansive mappings, J. Optim. Theory Appl., 139 (2008), pp. 403-418.  R. Glowinski and P. Le-Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM, Philadelphia, 1989.  S. Haubruge, V.H. Nguyen and J.J. Strodiot, Convergence analysis and applications of the Glowinski-Le-Tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. Optim. Theory Appl., 97 (1998), pp. 645-673.  F.Gu, Convergence theorems for \$phi\$-pseudocontractive type mappings in normed linear spaces, Northeast Math. J., 17 (2001), pp. 340-346.  F. Gu, Strong convergence of an implicit iteration process for a finite family of uniformly \$L\$-Lipschitzian mapping in Banach spaces, J. Ineq. and Appl., doi:10.1155/2010/801961.  S. Ishikawa, Fixed points by a new iteration method, Proceeding of the America Mathematical society, 4 (1974), pp. 157-150.  S.H. Khan and W. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn., 53 (2001), pp. 143-148.  S.H. Khan, I. Yildirim and M. Ozdemir, Some results for finite families of fniformly \$L\$-Lipschitzian mappings in Banach paces, Thai J. Math., 9 (2011), pp. 319-331.  J.K. Kim, D.R. Sahu and Y.M. Nam, Convergence theorems for fixed points of nearly uniformly \$L\$-Lipschitzian asymptotically generalized \$Phi\$-hemicontractive mappings, Nonlinear Anal., 71 (2009), pp. 2833-2838.  G. Lv, A. Rafiq and Z. Xue, Implicit iteration scheme for two phi-hemicontractive operators in arbitrary Banach spaces, Journal of Ineq. and Appl., 2013, 2013:521.  E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. 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Takahashi, Iterative methods for approximation of fixed points and their applications, J. Oper. Res. Soc. Jpn., 43 (2000), pp. 87-108.  W. Takahashi and T. Tamura, Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J. Approx. Theory, 91 (1997), pp. 386-397.  B.S. Thakur, Weak and strong convergence of composite implicit iteration process, Appl. Math. Comput., 190 (2007), pp. 965-973.  B.S. Thakur, Strong Convergence for Asymptotically generalized \$Phi\$-hemicontractive mappings, ROMAI J., 8 (2012), pp. 165-171.   H.K. Xu and R.G. Ori, An implicit iteration process for nonexpansive mapping, Num. Fun. Anal. Optim., 22 (2001), pp. 767-773.  Y. Yao, Convergence of three-step iterations for asymptotically nonexpansive mappings, Appl. Math. Comput., 187 (2007), pp. 883-892.  L. P. Yang, Convergence theorem of an implicit iteration process for asymptotically pseudocontractive mappings, Bull. of the Iran. Math. Soc., 38 (2012), pp. 699-713.  L.P. Yang and G. Hu, Convergence of implicit iteration process with random errors, Acta Math. Sinica (Chin. Ser.), 51 (2008), pp. 11-22.  L.C. Zeng, On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci., 23 (2003), pp. 31-37.  L.C. Zeng, On the iterative approximation for asymptotically pseudocontractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann., 26 (2005), pp. 283-290.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 248908 10.22130/scma.2021.521013.887 Research Paper New Integral Inequalities Relating to a General Integral Operators Through Monotone Functions New Integral Inequalities Relating to a General Integral Operators Through Monotone Functions Benaissa Bouharket Faculty of Material Sciences, University of Tiaret and Laboratory of Informatics and Mathematics, University of Tiaret-Algeria. Senouci Abdelkader Department of Mathematics, University of Tiaret and Laboratory of Informatics and Mathematics, University of Tiaret-Algeria. 01 02 2022 19 1 41 56 12 12 2020 08 01 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_248908.html

Weighted integral inequalities for general integral operators on monotone positive functions with parameters \$p\$ and \$q\$ are established in . The aim of this work is to extend the results to different cases of these parameters, in particular for negative \$p\$ and \$q\$. We give some new lemmas which will be frequently used in the proofs of the main theorems.

General integral operator Weighted inequalities Monotone functions Absolutely continuous
 M. Arino and B. Muckenhoupt,  Maximal function on classical Lorenz spaces and Hardy's inequality with weights for non-increasing functions, Trans. Amer. Math. Soc., 320 (1990), pp. 727-735.  B. Benaissa,  On the Reverse Minkowski's Integral Inequality, Kragujevac. J. Math., 46(3) (2022), pp. 407-416.  C. Bennett and R. Sharpley,  Interpolation of operators. Math. 129, Academic Press, 1988.   Shanzhong. Lai,  Weighted norm inequalities for general operators on monotone functions, Amer. Math. Soc., 340(2) (1993), pp. 811-836.  Bicheng. Yang,  On a new Hardy- type integral inequality, Int. Math. Forum., 2(67) (2007), pp. 3317-3322.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 248910 10.22130/scma.2021.533260.953 Research Paper The Operators' Theorems on Fuzzy Topological Spaces The Operators' Theorems on Fuzzy Topological Spaces Saheli Morteza Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Mohsenialhosseini Seyed Ali Mohammad Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Saedi Goraghani Hadi Department of Mathematics, Payame Noor University, Tehran, Iran. 01 02 2022 19 1 57 76 02 07 2021 08 12 2021 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_248910.html

Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationshipbetween fuzzy continuity of linear operators and fuzzy boundedness is investigated. The uniform boundedness theorem is then discussed, so too is the norm of a linear operator. Finally, the open mapping theorem is proved for each of the three defined fuzzy topologies, and the closed graph theorem is studied.

Fuzzy norm Fuzzy topology Fuzzy boundedness Fuzzy continuity
 M. Arunkumar and S. Karthikeyan, Solution and intuitionistic fuzzy stability of ndimensional quadratic functional equation: direct and flxed point methods, International Journal of Advanced Mathematical Sciences, 2 (1) (2014), pp. 21-33.  T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (3) (2003), pp. 687-705.  T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst., 151 (2005), pp. 513-547.  V. Chandrasekar, D. Sobana and A. Vadivel, On Fuzzy e-open Sets, Fuzzy e-continuity and Fuzzy e-compactness in Intuitionistic Fuzzy Topological Spaces, Sahand Commun. Math. Anal., 12 (1) (2018), pp. 131-153.  S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 8 (1994), pp. 429-436.  N.F. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets Syst., 107 (1999), pp. 349-354.  J.-X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets Syst., 157 (2006), pp. 2739-2750.  C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets Syst., 48 (1992), pp. 239-248.  O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst., 12 (1984), pp. 215-229.  I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), pp. 326-334.  A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12 (1984), pp. 143-154.  G. Lu, J. Xina, Y. Jinb and C. Park, Approximation of general Pexider functional inequalities in fuzzy Banach spaces, J. Nonlinear Sci. Appl., 12 (2019), pp. 206-216.  R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput., 17 (1-2) (2005), pp. 475-484.  I. Sadeqi and F. Solaty Kia, Fuzzy normed linear space and its topological structure, Chaos Solitons Fractals, 40 (2009), pp. 2576-2589.  M. Saheli, Fuzzy topology generated by fuzzy norm, Iran. J. Fuzzy Syst., 13 (4) (2016), pp. 113-123.  M. Saheli, On fuzzy topology and fuzzy norm, Ann. Fuzzy Math. Inform., 10 (4) (2015), pp. 639-647.  A. Vadivel and E. Elavarasan, On rarely generalized regular fuzzy continuous functions in fuzzy topological spaces, Sahand Commun. Math. Anal., 4 (1) (2016), pp. 101-108.  A. Vadivel and E. Elavarasan, r-fuzzy regular semi open sets in smooth topological spaces, Sahand Commun. Math. Anal., 6 (1) (2017), pp. 1-17.  J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets Syst., 133 (2003), pp. 389-399.  G.-H. Xu and J.-X. Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets Syst., 158 (2007), pp. 2375-2385.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 248968 10.22130/scma.2021.529567.933 Research Paper Some Results on Cesàro summability in Intuitionistic Fuzzy \$n\$-normed linear Spaces Some Results on Cesàro summability in Intuitionistic Fuzzy \$n\$-normed linear Spaces Debnath Pradip Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam - 788011, India. 01 02 2022 19 1 77 87 02 05 2021 03 01 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_248968.html

The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Cesàro summability in an intuitionistic fuzzy \$n\$-normed linear space (IFnNLS). We show that Cesàro summability method is regular in an IFnNLS, but  Cesàro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.

Intuitionistic fuzzy \$n\$-normed linear space Ces`{a}ro summability Tauberian theorem
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SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 249406 10.22130/scma.2022.545343.1038 Research Paper Categorical Properties of Down Closed Embeddings Categorical Properties of Down Closed Embeddings Shahbaz Leila Department of Mathematics, University of Maragheh, Maragheh, 55181-83111, Iran. 01 02 2022 19 1 89 99 22 12 2021 06 02 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_249406.html

Let \$mathcal M\$ be a  class of (mono)morphisms in a category \$mathcal A\$. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (\${mathcal A}\$,\${mathcal M}\$).In this paper, we take \$mathcal A\$ to be the category {bf Pos}-\$S\$ of \$S\$-posets over a posemigroup \$S\$, and \${mathcal M}_{dc}\$ to be the class of down closed embeddings and study the categorical properties, such as limits and colimits, of the  pair (\${mathcal A}\$,\${mathcal M}\$). Injectivity with respect to this class of monomorphisms have been studied by Shahbaz et al., who used it to obtain  information about regular injectivity.

\$S\$-poset Down closed embeddings dc-embeddings Limit Colimit
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SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 249417 10.22130/scma.2021.526207.918 Research Paper L\$_p\$-C\$^*\$-Semi-Inner Product Spaces L\$_p\$-C\$^*\$-Semi-Inner Product Spaces Khalili Zakiye Department of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran. Janfada Alireza Department of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran. Miri Mohammad Reza Department of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran. Niazi Mohsen Department of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran. 01 02 2022 19 1 101 117 06 03 2021 05 02 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_249417.html

This article introduces the notion of L\$_p\$-C\$^*\$-semi-inner product space, a generalization of the concept of C\$^*\$-semi-inner product space  introduced by Gamchi et al., where we consider H"{o}lder's inequality instead of Cauchy Schwartz' inequality. We establish some basic results L\$_p\$-C\$^*\$-semi-inner product spaces, analogous to those valid for C\$^*\$-semi-inner product spaces and Hilbert C\$^*\$-modules.

Hilbert C\$^*\$-module Semi-inner product derivation Anti-Derivation
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SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 249585 10.22130/scma.2021.527460.926 Research Paper Positivity of Integrals for Higher Order \$nabla-\$Convex and Completely Monotonic Functions Positivity of Integrals for Higher Order \$nabla-\$Convex and Completely Monotonic Functions Mehmood Faraz Department of Mathematics, Dawood University of Engineering and Technology, New M. A. Jinnah Road, Karachi-74800, Pakistan. Khan Asif Raza Department of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan. Adnan Muhammad Department of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan. 01 02 2022 19 1 119 137 03 04 2021 14 02 2022 Copyright © 2022, دانشگاه مراغه. 2022 https://scma.maragheh.ac.ir/article_249585.html

We extend the definitions of \$nabla-\$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals \$int P(y)f(y) dy\$ and \$int int P(y,z) f(y,z) dy   dz\$ are deduced. Using obtained identities, positivity of these expressions are characterized for  higher order \$nabla-\$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.

Convex functions \$nabla-\$convex functions completely monotonic functions
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