[PDF] Top 20 Common best proximity point theorem for multivalued mappings in partially ordered metric spaces

... In this section, we give some basic definitions and notions that will be used frequently. Let X be a nonempty set such that (X, d, ) is a partially ordered metric space. Consider A and B to be ... See full document

... a multivalued mapping under a more general contractive condition in partially ordered metric ...main theorem are also given. The second section is devoted for common ... See full document

... Obviously, Theorem . is an extensive version of the Banach contraction principle. Re- cently, the generalized contraction principle has been studied by many authors in metric spaces or more ... See full document

... of best proximity points is an interesting topic of optimization theory which recently attracted the attention of many authors (see [7, 18, 27, 29, 30, 31, 33, 51, 52, 53, 54, 55, ...of best ... See full document

... fixed point for the mapping F, and successfully applied their results to the problem of existence and uniqueness of solution for a periodic boundary value ... See full document

... of best proximity point is an important aspect of optimization ...Lipschitzian mappings on a partially ordered metric ...of best proximity points for these ... See full document

... Fixed point theory is essential for solving various equations of the form Tx = x for self- mappings T defined on subsets of metric spaces or normed linear ...a metric space and a ... See full document

... fixed point theorem for contraction mappings has been generalized and extended in many directions ...in partially ordered metric ... See full document

... of best proximity points for a new class of non-self mappings involving simulation functions in a metric space endowed with a partial ...fixed point results via simulation functions are ... See full document

... A best proximity point represents an optimal approximate solution to the equation T x = x whenever a non-self-mapping T has no fixed ...fixed point coincides with a best ... See full document

... fixed point theorem of nonlinear contraction mappings with mixed monotone property in partially ordered G-metric ...coupled common fixed point results for a mixed ... See full document

... fixed point problems, and their allied problems, have attracted a large general interest amongst mathematician after the appearance of the work of Gnana Bhaskar and Lakshmikantham [] in  in which a coupled ... See full document

... Fixed point theory have an important role in many branches of mathematics such as differential and integral equations, optimization and variational ...fixed point equation T x = x, where T : A → B is some ... See full document

... Passing to limit n → ∞, we obtain d(z, T z) = d(A, B). Similarity, we also derive d(Sz, z) = d(A, B). Case 2: We will show that T or S have best proximity points in A and B, respectively. Under the ... See full document

... fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric ...deduce best proximity and fixed ... See full document

... Then (x ∗ , y ∗ ) ∈ K × K is a solution of the system of variational inequalities (.). Since A, B are continuous, so the set of solutions of (.) is closed. This completes the proof. It is obvious that Theorem ... See full document

... fixed point, provided that the metric space (X , d) is ...[1, Theorem 3.5], Banach’s con- traction theorem has been generalized for two self-maps T : X → X and S : X → ...in metric ... See full document

... Theorem . Let K be a nonempty, compact and convex subset of a normed space E. Then for any continuous mapping T : K → E , there exists x ∈ K with x – T x = inf y∈K T x – y. Some generalizations and extensions of ... See full document

... function spaces of the Lebesgue type L p were made in the early s by Orlicz and Birnbaum in connection with orthogonal expan- ...considering spaces of functions with some growth properties different from ... See full document

... fixed point and obtained some fixed point theorems for contractive type maps in partially ordeded metric ...unique common triple fixed point theorem for two maps by using ... See full document