In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,a...In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,and some novel results are derived.The discovered results generalize previously known results in the context of a double controlled metric type space environment.This article’s proximity point results are the first of their kind in the realm of controlled metric spaces.To build on the results achieved in this article,we present an application demonstrating the usability of the given results.展开更多
A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is intro...A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.展开更多
In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the c...In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.展开更多
文摘In this study,we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces.A non-trivial example is given to elucidate our analysis,and some novel results are derived.The discovered results generalize previously known results in the context of a double controlled metric type space environment.This article’s proximity point results are the first of their kind in the realm of controlled metric spaces.To build on the results achieved in this article,we present an application demonstrating the usability of the given results.
基金Project supported by the Scientific Research Fund of Sichuan Normal University(No.09ZDL04)the Sichuan Province Leading Academic Discipline Project(No.SZD0406)
文摘A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.
文摘In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.
