For a given mapping f in the framework of different spaces, fixed-point equations form fx=x can model several problems areas, such as differential equations, optimization, and computer science. In this work, aim is to find best proximity point prove its uniqueness on partial metric spaces where symmetry condition preserved for types contractive non-self endowed with graph. Our theorems generali...

The main objective of the paper is to prove some unified common fixed point theorems for a family mappings under minimal set sufficient conditions. Our results subsume and improve host contractive type available in literature metric theory. Simultaneously, we provide new answers general framework problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding existence definition which stro...

As the generalization of fixed-point theory, fixed-circle problems are interesting and notable geometric constructions. In this paper, we prove that some new necessary conditions investigated for existence a fixed circle given self-mapping in G -metric spaces. The well-known Braincari Chatterj...

Let C be a closed convex subset of a Hilbert space H , let {T (t) : t ≥ 0}be a strongly continuous semigroup of non-expansive mapping on C such that ⋂ t≥0 F (T (t)) = ∅, and f : C → C be a fixed contractive mapping. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn tn = 0. Define a sequence {xn} in C by xn = αnf(xn) + (1 − αn)T (tn)xn, for n ∈ N....

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F T / ∅. Let {λn} ⊂ 0, 1/2 be a seq...

Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ...

An affine iterated function system (IFS, [4]) over the reals is given by a set of contractive affine transformations on a complete metric space R for some positive natural number k. Thus an interesting problem is to decide, whether a given matrix M describes a contraction mapping, i.e. whether there exists some s < 1 such that |Mz| ≤ s|z| for each z ∈ R, where | · | denotes the Euclidean norm. ...

In this paper, we prove that if f is a contractive closed-valued correspondence on a cone metric space (X, d) and there is a contractive orbit {xn} for f at x0 ∈ X such that both {xni} and {xni+1} converge for some subsequence {xni} of {xn}, then f has a fixed point, which generalizes a fixed point theorem for contractive closed-valued correspondences from metric spaces to cone metric spaces.