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The aim of this paper is to define a Berinde type ( ρ , μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich's extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in X, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors. [ABSTRACT FROM AUTHOR]

We establish some fixed point theorems for a-admissible mappings in the context of metric-like space via various auxiliary functions. In particular, we prove the existence of a fixed point of the generalized Meir-Keeler type α-ø-contractive self-mapping f defined on a metric-like space X. The given results generalize, improve, and unify several fixed point theorems for the generalized cyclic contractive mappings that have appeared recently in the literature. [ABSTRACT FROM AUTHOR]

Based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive operator, which is also a unique solution of a variational inequality. Under suitable assumptions, we study the strong convergence of the sequences generated by the proposed algorithms. The results of this paper improve and extend several known results in the literature. [ABSTRACT FROM AUTHOR]

We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich's extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature. [ABSTRACT FROM AUTHOR]

Formulation of uncertainty Volterra integrodifferential equations (VIDEs) is very important issue in applied sciences and engineering; whilst the natural way to model such dynamical systems is to use the fuzzy approach. In this work, we present and prove the existence and uniqueness of four solutions of fuzzy VIDEs based on the Hausdorff distance under the assumption of strongly generalized differentiability for the fuzzy-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported fuzzy sets in . In addition to that, we utilize and prove the characterization theorem for solutions of fuzzy VIDEs which allow us to translate a fuzzy VIDE into a system of crisp equations. The proof methodology is based on the assumption of the generalized Lipchitz property for each nonlinear term appears in the fuzzy equation subject to the specific metric used, while the main tools employed in the analysis are founded on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. [ABSTRACT FROM AUTHOR]