F -contraction has been a widely investigated problem in the Fixed Point Theory during the last decade.There are different results regarding generalizations and modifications of Fcontraction in various settings, along with the results concerning application of those concepts, mostly in the area of differential and difference equations, fractional calculus, etc.In this paper, it will be shown that there are abundant requests regarding the definition of F -contraction.In this way, the wider class of F contraction is formed and, for this new type of contraction, called simple F -contraction or sF -contraction, we prove the existence and uniqueness of the fixed point on a complete metric space.Similar results are derived for the modified concept of F -Suzuki contraction.

The ultimate goal of this paper is to investigate the approximation of involution in fuzzy C * -algebra.If A is fuzzy Banach algebra and f is function which defined on it, we prove that under conditions A has unique involution.In this case, fuzzy Banach algebra A can be evolute to Fuzzy C * -algebra.For this purpose, we use the Hyers-Ulam-Rassias stability method and the fixed point technique.

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions. Finally, using MATLAB software, we provide some numerical examples to illustrate our results.

The well-known Kirk [8] fixed point theorem for nonexpansive mapping relies on the geometric notion called normal structure property.Ghde [5] provided sufficient conditions for the existence of a fixed point of a nonexpansive mapping without using normal structure property.In [4], Kirk et.al.introduced a notion called relatively nonexpansive mapping and provided sufficient conditions for the existence of best proximity points for such mappings using the proximal normal structure property.The main result of this manuscript provides the existence of best proximity points of a relatively nonexpansive mapping without using the proximal normal structure property.Also, our main result extends Ghde's fixed point theorem in best proximity point setting.An example is given to illustrate our main result.

In this paper, we prove a general fixed point theorem for ultrametric n-Banach spaces. We also show its applications in proving the hyperstability, in the sense of Gȃvrut ¸ȃ, of the following monomial functional equation where

In this paper, we introduce α-nonexpansive multi-valued mappings in Hilbert spaces, and prove some properties and the existence of fixed points of these mappings. Further, we apply the Fan-KKM theorem to prove the existence of solutions to split equilibrium problems. Then we study iterative schemes for solving split equilibrium problems and common fixed point problems of a finite family of α-nonexpansive multi-valued mappings in Hilbert spaces. we prove that the proposed iterative algorithms converge weakly and strongly to a common solution of the considered problems. Our results improve and extend the previous results given in the literature.

In this work, we consider a general model of fractional differential variational inequalities formulated by a fractional differential inclusion and a general variational inequality. The existence of mild solutions on a half-line is proved. Furthermore, we study establish the sufficient conditions ensuring the existence and uniqueness of asymptotically periodic solutions based on theory of semigroup and some fixed point arguments. Finally, examples are given to illustrate our theoretical results.

The purpose of this paper is to establish a general fixed point theorem for mean nonexpansive multivalued mappings defined on weakly compact and convex subsets of Banach spaces with property (D).The main result obtained in this paper significantly extends and improves many of the well-known results in the existing literature.