[PDF] Top 20 \(C^{*}\) Valued G contractions and fixed points

... d(Tx, Ty) A ∗ d(x, y)A, for all x, y ∈ X. () Observe that the right hand side of () is defined because A is an algebra, not necessar- ily real. Also, observe that it is not necessary that one can define an involution ... See full document

... Mappings satisfying the inequality (1.1) with a = 1 and b = c = 0 is called nonexpan- sive and it was considered by Kirk [6], whereas the mapping with a = 0, b = c = 1/2 by Wong [13]. Recently, Fisher et ... See full document

... ordered g-contraction is introduced, and some fixed and common fixed point theorems for g-nondecreasing ordered g-contraction mapping in partially ordered metric spaces are ...ordered ... See full document

... Definition . A square matrix of real numbers is said to be convergent to zero if and only if its spectral radius ρ(A) is strictly less than . In other words, this means that all the eigenvalues of A are in the open ... See full document

... It is clear that Proposition  does not characterize metric aggregation functions because there are metric aggregation functions that are not monotone (see Example  in []). In- spired by this fact, Borsík and Doboš ... See full document

... (C) If T is left (right) partially J -admissible in w  , if T is left (right) P -quasi-closed on B L– J (w  , r) (B R– J (w  , r)) and if (X, P ) is a Hausdorff space, then there exists w ∈ X such that Fix(T ) = ... See full document

... of fixed point theory in metric spaces and has intensified in the past few decades: (a) the existence and uniqueness of fixed points of various generalizations of Banach and Kannan contrac- tions; ... See full document

... integral G-contraction with contraction constant c = +p  . Note that G is a weakly connected (C)-graph and ...Banach G-contraction since, for ( n+  , n  ) ∈ ... See full document

... and g are weakly compatible mappings, then we have fq = fgp = gfp = gq, that is, q is the coincidence point of f and ...and g, so fq = gq = ..., g : X → X ... See full document

... multivalued contractions in complete metric spaces are introduced, and the conditions guaranteeing the existence of fixed points for the multivalued contractions are ...few fixed point ... See full document

... one fixed point for quasi–contractions when α ∈ [ 1 2 , 1) but no clear answer exists right now and many of them either have failed or changed to a lighter ...strict fixed point results in the set of ... See full document

... Example 2.4. Let E : R and P : R . Put A : 1, 3 and B : 1, 4 so A B, B A but A / B. Theorem 2.5. Let M, d be a complete cone metric space, T : M → CM, a set-valued map and the function f : M → P defined by fx dx, ... See full document

... In , Kada et al. [] introduced the concept of w-distance and got some fixed point theorems for single-valued mappings under w-distance. In , Feng and Liu [, Theo- rem .] proved the following fixed point ... See full document

... Theorem 2.19. Let M be a nonempty subset of a normed (resp., Banach) space X and let T, f, g be self-mappings of M. Suppose that Ff ∩ Fg is q-starshaped, cl TFf ∩ Fg ⊆ Ff ∩ Fg (resp., wcl TFf ∩ Fg ⊆ Ff ∩ Fg), clTM ... See full document

... It is clear that a Picard operator is a weakly Picard one but the identity mapping of any metric space with more that one point shows that the converse is not generally true. In fact, the set of fixed ... See full document

... concepts: fixed points, strict fixed points, periodic points, strict periodic points, multivalued Picard and weakly Picard operators; data dependence of the fixed point ... See full document

... A recent research direction in fixed-point theory is the study of the fixed-point problem for single-valued and multivalued operators in the context of a metric space endowed with a graph. This approach was recently ... See full document

... Recently, there have been so many exciting developments in the field of existence of fixed points in partially ordered sets. For instance, Ran and Reurings [] extended the Banach contraction principle in partially ... See full document

... In [1 I, [2 l, Sehgal and Smithson proved fixed point theorems for set-valued weak drectional contractions which extend earlier rosults of Clarke [3], Kirk and Ray [4], In the present pa[r] ... See full document

... In this paper, we generalize some main results of (Jachymski in Proc. Am. Math. Soc. 136:1359-1373, 2008) from metric to uniform spaces endowed with an E -distance and a graph using a new type of contractions by ... See full document