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In this paper, we establish the Caccioppoli estimates for the nonlinear differential equation − D ‾ (| D v | p − 2 D v) = λ | v | p − 2 v , 1 < p < ∞ , where D is the Dirac operator. Moreover, we obtain general weighted versions of the Caccioppoli-type inequalities for the Dirac operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings. [ABSTRACT FROM AUTHOR]

In this paper, we consider two families Ψ1 and Ψ2 of mappings defined on [0,+∞) satisfy some certain properties. Using the mentioned properties for Ψ1 and Ψ2, we prove the analogous PPF dependent fixed point theorems for mappings as in Drici et al. (Nonlinear Anal. 67:641-647, 2007) in partially ordered Banach spaces where mappings satisfy the weaker contractive conditions without assuming the topological closedness with respect to the norm topology for the Razumikhin class Rc. [ABSTRACT FROM AUTHOR]

In this paper, using fixed-point index theory and approximation techniques, we consider the existence and multiplicity of fixed points of some nonlinear operators with singular perturbation. As an application we consider the existence and multiplicity of positive solutions of singular systems of multi-point boundary value problems, which improve the results in the literature. [ABSTRACT FROM AUTHOR]

The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established. [ABSTRACT FROM AUTHOR]

The present paper deals with the common solution method for finding a fixed point of a nonexpansive mapping and a solution of split hierarchical Minty variational inequality problems. We discuss the weak convergence of the sequences generated by the proposed method to a common solution of a fixed point problem and a split hierarchical Minty variational inequality problem. An example is presented to illustrate the proposed algorithm and result. [ABSTRACT FROM AUTHOR]

In this paper, we study strong and △-convergence of a newly defined three-step iteration process for nearly asymptotically nonexpansive mappings in the setting of $\operatorname{CAT}(k)$ spaces. Our results generalize, unify and extend many known results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of integral equations and apply the coincidence and common fixed point theorems for four mappings satisfying a (ψ, α, β)-weakly contractive condition in ordered metric spaces to prove the existence of a common solution to integral equations. Also we furnish suitable examples to demonstrate the validity of the hypotheses of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of an α3-proximal admissible mappings and establish the existence of best proximity point theorems for implicit relation type modified α3-proximal contractions. As applications of our theorems, we derive some new best proximity point results for implicit relation type contractions whenever the range space is endowed with a graph or with a partial order. The obtained results generalize, extend, and modify some best proximity point results in the literature. Several interesting consequences of our theorems are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we study on q-Stancu-Szasz-Beta type operators. We give these operators convergence properties and obtain a weighted approximation theorem in the interval [0,∞). [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish certain new fixed point results for multi-valued as well as single-valued maps satisfying an α-ψ-contractive conditions in complete metric space. As an application, we derive some new fixed point theorems for ψ-graphic contractions defined on a metric space endowed with a graph as well as an ordered metric space. The presented results complement and extend some very recent results proved by Asl et al. (Fixed Point Theory Appl. 2012:212, 2012) and Samet et al. (Nonlinear Anal. 75:2154-2165, 2012) as well as other theorems given by Hussain et al. (Fixed Point Theory Appl. 2013:212, 2013). Some comparative examples are constructed which illustrate the superiority of our results to the existing ones in the literature. [ABSTRACT FROM AUTHOR]

The article provides an overview of the study which examines the locally uniform nonsquare in generalized Cesàro sequence spaces. It found that the generalized Cesàro sequence spaces possessed the locally uniform nonsquare and have the fixed point property, but they are not uniformly nonsquare. It specified that the result is related to the result of the paper J. False and colleagues in 2006. It was done through giving examples and the motivation to find the geometric properties that are weaker than uniformly nonsquare, but still possessed the fixed point property in any Banach spaces .

The article focuses on the introduction of neutrosophic continuity and neutrosophic boundedness, which is a fair extension of intuitionistic fuzzy continuity and intuitionistic fuzzy boundedness, respectively. The article further advances to illustrate the Fréchet derivative of nonlinear operators between neutrosophic normed spaces (NNS). Examples have been provided in compliance with the theory with the aid of some standard sequence spaces. [ABSTRACT FROM AUTHOR]

We recall the concepts of {α, ξ}-contractive and α-admissible mappings on complete metric spaces to state related fixed point theorems. In this paper, we obtain some fixed point results for {α, ξ}-expansive locally contractive mappings in complete metric spaces. The contractiveness of the mapping is only on a closed ball instead of the whole space. Our results unify, generalize, and complement various well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has been recommended and solved by employing an iterative algorithm. We establish the equivalence between nonlinear fuzzy ordered variational inclusion problem and nonlinear fuzzy ordered resolvent equation problem. The existence and convergence analysis of the solution of nonlinear fuzzy ordered variational inclusion problem involving XOR operation has been substantiated by applying a new resolvent operator method with XOR operation technique. The iterative algorithm and results demonstrated in this article have witnessed a significant improvement in many previously known results of this domain. [ABSTRACT FROM AUTHOR]

Let X be a uniformly convex and q-uniformly smooth Banach space with 1 < q ≤ 2 . In the framework of this space, we are concerned with a composite gradient-like implicit rule for solving a hierarchical monotone variational inequality with the constraints of a system of monotone variational inequalities, a variational inclusion and a common fixed point problem of a countable family of nonlinear operators { S n } n = 0 ∞ . Our rule is based on the Korpelevich extragradient method, the perturbation mapping, and the W-mappings constructed by { S n } n = 0 ∞ . [ABSTRACT FROM AUTHOR]

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given. [ABSTRACT FROM AUTHOR]

In this work, we prove some new generalizations of Smarzewski's fixed point theorem and some new fixed point theorems which are original and quite different from the well-known results in the literature. [ABSTRACT FROM AUTHOR]

Sufficient conditions are obtained on two given logharmonic mappings f1 and f2 that ensure the product F(z) = fλ1 (z)f 1-λ2 (z), 0 ≤ λ ≤ 1, is a univalent starlike logharmonic mapping. Several illustrative examples are constructed from this product. [ABSTRACT FROM AUTHOR]

In this article, we prove a best proximity point theorem for generalized cyclic contractions in convex metric spaces. Then we investigate the structure of minimal sets of cyclic relatively nonexpansive mappings in the setting of convex metric spaces. In this way, we obtain an extension of the Goebel-Karlovitz lemma, which is a key lemma in fixed point theory. [ABSTRACT FROM AUTHOR]

Considering α-admissible mappings in the setup of partial b-metric spaces, we establish some fixed and common fixed point results for ordered cyclic weakly (ψ, ϕ, L, A, B)-contractive mappings in complete ordered partial b-metric spaces. Our results extend several known results in the literature. Examples are also provided in support of our results. [ABSTRACT FROM AUTHOR]

In this article, we obtain the demiclosed principle, fixed point theorems and convergence theorems for the class of total asymptotically nonexpansive mappings on CAT(κ) spaces with κ > 0. Our results generalize the results of Chang et al. (Appl. Math. Comput. 219:2611-2617, 2012), Tang et al. (Abstr. Appl. Anal. 2012:965751, 2012), Karapınar et al. (J. Appl. Math. 2014:738150, 2014) and many others. [ABSTRACT FROM AUTHOR]

The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term utt - Σnt=1(∂/∂xi)(∣∂u/∂xi∣p-2(∂u/∂xi))+a∣ut∣q-2ut = b∣u∣r-2u in a bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in W1,p0 (Ω) and show the asymptotic behavior of the global solutions through the use of an important lemma of Komornik. [ABSTRACT FROM AUTHOR]

In this short note we point out that the recently announced notion, the $C^{*}$-valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the $C^{*}$-valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems. [ABSTRACT FROM AUTHOR]

The article discusses a study on the approximation of fixed points of nonexpansive mappings and the solutions of variational inequalities. It states that a convergence theorem connected to finite family of nonexpansive maps is proven. It mentions that in Hilbert spaces, accretive operators are referred to as monotone where inequalities and hold with jq replaced by the identity map of H. It further states that the study aims to modify schemes and prove strong convergence theorems for the solution of the variational inequality.

The article strong convergence theorems for approximation of common fixed points for a finite family of pseudocontractive mappings. It states that the approximation of an implicit iteration algorithm are proven in Banach spaces. Mathematicians introduce an implicit iteration process for a family of nonexpensive mappings which is illustrated in mathematical notation. On the other hand, other mathematicians proved the weak convergence of iterative process to a common fixed point of a finite family nonexpansive mappings in a Hilbert space.

The article examines a new algorithm for a universal scheme for relaxed cocoercive nonlinear inequalities that affects three dissimilar operators in Hilbert spaces by the convergence of projection method. Solutions of the system of nonlinear relaxed cocoercive variational inequalities are also discussed within the section. Such mathematical inequalities are said to be common fixed points of three different quasi-nonexpansive mappings, which were also considered in the study. Research results of the study include the previous results of other research efforts on the subject, as to extend and improve the main results of former study.

The article introduces an extragradient procedure for fixed point problems and variational inequality problems. With the use of this procedure the common element of the set of fixed points of a non-expansive mapping and the set of solutions of the variational inequality for monotone mapping can be determined. The section denotes on various research results regarding the method and explains how the different studies improve the researchers' understanding of the subject. It also offers computations given by the author, illustrating how they arrived to their conclusion.

The article proposes and examines an iterative algorithm for a finite family of non-expansive mappings T1, T2, …, Tr. The study uses various iterative schemes to examine a common fixed point of a finite family of non-expansive mappings under some type of control conditions. It reveals that the proposed iterative algorithm converges strongly to a common fixed point of T1, T2, …, Tr. The section also provides computations of the problem and explains how they arrived to their conclusion.

The notion of nonlinear (F s , L) -contractive multivalued operators is initiated and some related fixed point results are considered. We also give an example to show the validity of obtained theoretical results. Our results generalize many existing ones in the literature. [ABSTRACT FROM AUTHOR]