where / is a mapping of X into its adjoint space X* such that for all u in X, (J(u)} ^)=|M| 2 d ||/(^)|| HMI* In some recent papers ([7], [8], [9]), we have presented an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings. These results were obtained by interweaving the fixed point theory of nonexpans...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

Throughout this paper, G will denote a nondegenerate continuous collection of atriodic continuous curves (i.e. arcs or simple closed curves) filling up a compact metric continuum M. As is well known, we may regard G itself as a compact metric continuum, with the elements of the collection G as the points of the space G and with G, as a space, the image of M under an open continuous mapping whos...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

For simplicity, we adopt the following convention: a, b, c, d, r1, r2, r3, r, r4, s1, s2 are real numbers, p, q are points of E 2 T , P is a subset of the carrier of E2 T , and X, Y , Z are non empty topological spaces. Next we state a number of propositions: (1) For all a, b, c holds c ∈ [a, b] iff a ¬ c and c ¬ b. (2) Let f be a continuous mapping from X into Y and g be a continuous mapping f...

We prove that if a mapping F : X → → Y , where X and Y are Banach spaces, is metrically regular at x̄ for ȳ and its inverse F−1 is convex and closed valued locally around (x̄, ȳ), then for any function G : X → Y with lipG(x̄) · regF (x̄ | ȳ)) < 1, the mapping (F + G)−1 has a continuous local selection x(·) around (x̄, ȳ + G(x̄)) which is also calm.

In this paper, we present two new generalizations of the pasting lemma using soft mixed structure. To do this, introduce notions a $(\tau _{1},\tau _{2})$-$g$-closed set and _{2})$-$gpr$% -closed set. We establish $g$-soft continuity $gpr$-soft between topological spaces $(X,\tau _{1},\Delta _{1})$, _{2},\Delta _{1})$ space ,\Delta _{2})$. Finally prove versions continuous mapping mapping.

In this paper we prove the existence of solutions to the following third order differential inclusion:  x(3)(t) ∈ F (t, x(t), ẋ(t), ẍ(t)) + G(x(t), ẋ(t), ẍ(t)), a.e. on [0, T ] x(0) = x0, ẋ(0) = u0, ẍ(0) = v0, and ẍ(t) ∈ S,∀t ∈ [0, T ], where F : [0, T ]×H×H×H → H is a continuous set-valued mapping, G : H× H × H → H is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂g(z) where g...