فهرست مطالب
 Volume:17 Issue: 2, 2020
 تاریخ انتشار: 1399/04/29
 تعداد عناوین: 12

Pages 122In this paper, we introduce two iterative schemes by a modified KrasnoselskiiMann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimumnorm element of the above two sets. Finally, some applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.Keywords: Multivalued mappings, Equilibrium problems, Iterative methods, Applications

Pages 2336In this paper, we present some fixed point theorems for single valued mappings on $K$complete, $M$complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$class and $A$class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.Keywords: Quasi metric space, left $K$Cauchy sequence, left $mathcal{K}$completeness, Fixed point

Pages 3753Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. Some applications for linear and nonlinear matrix equations are given.Keywords: Fixed points, Coupled fixed point, Coupled coincidence fixed Point, Generalized metric

Pages 5568In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic Afactor block circulant matrices are investigated.Keywords: Field of values, Perturbation, Matrix polynomial, companion linearization, Basic $A$factor block circulant matrix

Pages 6982In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variationallike inequality, the Stampacchia vector variationallike inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector variationallike inequalities and vector optimization problems are established.Keywords: Nonsmooth functions, Limiting subdifferential, Pseudoinvex functions, Vector variationallike inequalities, Vector optimization problems

Pages 83105Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complexvalued $S$metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$metric space. To do this, we prove some common fixed point (resp. fixed point) theorems using different techniques by means of new generalized contractive conditions and the notion of the closed ball. Our results generalize and improve some known fixed point results. We provide some illustrative examples to show the validity of our definitions and fixedpoint theorems.Keywords: $S$metric space, Fixed point theorem, Common fixed point theorem, Complex valued $S$metric space

Pages 107117In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods by combining the resolvent method with Halpern's iterative method and viscosity approximation method for finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations in CAT(0) metric spaces.Keywords: Monotone mapping, Nonexpansive mapping, Variational inequality, Fixed point, CAT(0) metric space

Pages 119138Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 4353] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$ contraction mappings andto prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $Theta$contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.Keywords: Almost contraction, $Theta$contraction, best proximity points, differential equation

Pages 139159By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the EdmundsonLahRibariv c inequality for solidarities that hold for a class of $n$convex functions. As an application, main results are applied to some operator means and relative operator entropy.Keywords: Solidarities_Ando's inequality_EdmundsonLahRibariv c inequality_$n$convex functions_Operator means

Pages 161171In this paper, at first, we introduce $alpha_{mu}$admissible, $Z_mu$contraction and $N_{mu}$contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions via $alpha$admissible simulation mappings, as well. Our results can be viewed as extension of the corresponding results in this area. Moreover, some examples and an application to functional integral equations are given to support the obtained results.Keywords: Measure of noncompactness, Simulation functions, $alpha$admissible mappings, Fixed point

Pages 173183In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.Keywords: Locally convex cones, Bornological convergence, Bornological cones, Bornological completion

Pages 185201In this note, the notion of generalized continuous K frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$frames. A necessary and sufficient condition for the existence of a generalized continuous $K$frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$frame for $ mathcal{H} $ with respect to $ mu $ is given. Also, a sufficient condition for a generalized continuous $K$frame is given. Further, among other results, we prove that generalized continuous $K$frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$frames and obtain conditions for the stability of generalized continuous $K$frames.Keywords: Frames, $K$frames, Continuous frames