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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]

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 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]

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 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]