Search results for "Weak"
showing 10 items of 1417 documents
Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dyn…
2013
In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.
Some fixed point theorems for generalized contractive mappings in complete metric spaces
2015
We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.
Common fixed points in generalized metric spaces
2012
Abstract We establish some common fixed point theorems for mappings satisfying a ( ψ , φ ) -weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature.
On the operators which are invertible modulo an operator ideal
2001
Atkinson [3] studied the operators which are left invertible $i(X, Y) or right invertible $T{X, Y) modulo /C, with K. the compact operators. He proved that an operator T € C(X, Y) belongs to <£/ or $ r if and only if the kernel and the range of T are complemented and additionally, the kernel is finite dimensional or the range is finite codimensional, respectively. Yood [19] obtained some perturbation results for these classes and Lebow and Schechter [12] proved that the inessential operators form the perturbation class for $,(A") and $r{X). Yang [18] extended some results of ^3, 19] to operators invertible modulo W, with W the weakly compact operators. His aim was to study a generalised Fre…
A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A
2013
In view of the fact that the fixed point theory provides an efficient tool in many fields of pure and applied sciences, we use the notion of the property E.A to prove a common fixed point theorem for weakly compatible mappings. The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.
JH-Operators and Occasionally Weakly g-Biased Pairs in Fuzzy Symmetric Spaces
2013
We introduce the notions of $\mathcal{JH}$-operators and occasionally weakly $g$-biased mappings in fuzzy symmetric spaces to prove common fixed point theorems for self-mappings satisfying a generalized mixed contractive condition. We also prove analogous results for two pairs of $\mathcal{JH}$-operators by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. We give also an application of our results to product spaces.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
2013
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions
2017
Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.
Restricted weak type on maximal linear and multilinear integral maps
2006
It is shown that multilinear operators of the form T ( f 1 , . . . , f k ) ( x ) T(f_1,...,f_k)(x) = ∫ R n K ( x , y 1 , . . . , y k ) f 1 ( y 1 ) . . . f k ( y k ) d y 1 . . . d y k =\!\int _{\mathbb {R}^n}\!K(x,y_1,...,y_k)f_1(y_1)... f_k(y_k)dy_1...dy_k of restricted weak type ( 1 , . . . , 1 , q ) (1,...,1,q) are always of weak type ( 1 , . . . , 1 , q ) (1,...,1,q) whenever the map x → K x x\to K_x is a locally integrable L 1 ( R n ) L^1(\mathbb {R}^n) -valued function.
Semi-compatible and reciprocally continuous maps in weak non-Archimedean Menger PM-spaces
2012
In this paper, we introduce semi-compatible maps and reciprocally continuous maps in weak non-Archimedean PM-spaces and establish a common fixed point theorem for such maps. Moreover, we show that, in the context of reciprocal continuity, the notions of compatibility and semi-compatibility of maps become equivalent. Our result generalizes several fixed point theorems in the sense that all maps involved in the theorem can be discontinuous even at the common fixed point.