\$r\$-fuzzy regular semi open sets in smooth topological spaces Appachi Vadivel Department of Mathematics, Annamalai University, Annamalai Nagar-608002, Tamil Nadu, India. author Elangovan Elavarasan Department of Mathematics, Annamalai University, Annamalai Nagar-608002, Tamil Nadu, India. author text article 2017 eng In this paper, we introduce and study the concept of \$r\$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using \$r\$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely \$r\$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the relationship among fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 1 17 https://scma.maragheh.ac.ir/article_22080_6b6d5d86c4a101f32db67cdc439daa70.pdf dx.doi.org/10.22130/scma.2017.22080 Dynamic equivalence relation on the fuzzy measure algebras Roya Ghasemkhani Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran. author Uosef Mohammadi Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran. author text article 2017 eng The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is complete. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 19 28 https://scma.maragheh.ac.ir/article_22015_386a0c0212ed48b855025307bda3aa1e.pdf dx.doi.org/10.22130/scma.2017.22015 Fuzzy weakly \$e\$-closed functions Veerappan Chandrasekar Department of Mathematics, Kandaswami Kandar&#039;s College, P-velur, Tamil Nadu-638 182, India. author Somasundaram Parimala Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar&#039;s College, P-velur, Tamil Nadu-638 182, India. author text article 2017 eng In this paper, we introduce and characterize fuzzy wea-kly \$e\$-closed functions in fuzzy topological spaces and the relationship between these mappings and some properties of them are investigated. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 29 37 https://scma.maragheh.ac.ir/article_23649_83ca0155b8a1e0d756e5be1c689630fe.pdf dx.doi.org/10.22130/scma.2017.23649 Fixed point results in cone metric spaces endowed with a graph Kamal Fallahi Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. author Ghasem Soleimani Rad Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. author text article 2017 eng In this paper, we prove the existence of fixed point for Chatterjea type mappings under \$c\$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on \$c\$-distance in metric and cone metric spaces. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 39 47 https://scma.maragheh.ac.ir/article_23163_0b45f04bdebc0d3a7cfa6e52d1e52803.pdf dx.doi.org/10.22130/scma.2017.23163 Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces Ebrahim Soori Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran. author text article 2017 eng This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solution of the variational inequality on the solution of systems of equilibrium problems and the common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 49 68 https://scma.maragheh.ac.ir/article_22988_6164b5942bd9d9914849f5c337fac6fa.pdf dx.doi.org/10.22130/scma.2017.22988 The analytical solutions for Volterra integro-differential equations within Local fractional operators by Yang-Laplace transform Hassan Kamil Jassim Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq. author text article 2017 eng In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution with less computation as compared with local fractional variational iteration method. Some illustrative examples are discussed. The results show that the methodology is very efficient and a simple tool for solving integral equations. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 69 76 https://scma.maragheh.ac.ir/article_23686_f3ebd1266c52fc8a3318ef0f1567e9cc.pdf dx.doi.org/10.22130/scma.2017.23686 A generalization of Kannan and Chatterjea fixed point theorems on complete \$b\$-metric spaces Hamid Faraji Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. author Kourosh Nourouzi Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran. author text article 2017 eng In this paper, we give some results on the common fixed point of self-mappings defined on complete \$b\$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete \$b\$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results. Sahand Communications in Mathematical Analysis University of Maragheh 2322-5807 06 v. 1 no. 2017 77 86 https://scma.maragheh.ac.ir/article_23831_6c258f4180145f5370b887cf815cd897.pdf dx.doi.org/10.22130/scma.2017.23831