In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

and Applied Analysis 3 In the sequel, let q > 1 4p and . . . , φ, ψ, φ, ψ, . . . the unique prime period-two solution of 1.1 with φ < ψ. Define f ∈ C φ, ψ × φ, ψ , φ, ψ by f ( x, y ) p y qx y 2.2 for any x, y ∈ φ, ψ and g ∈ C φ, ψ , φ, ψ by y∗ g ( y ) p y − y2 qy 2.3 for any y ∈ φ, ψ . Then

Let ψ : X → Y be a proper morphism with connected fibers from a smooth projective variety X onto a normal variety Y , i.e. a contraction. If −KX is ψ-ample, then ψ is said to be an extremal contraction and if moreover Pic(X)/ψ(Pic(Y )) ≃ Z then ψ is said to be an elementary extremal contraction or a Fano-Mori contraction. Usually contractions are divided into two types: birational and of fiber ...

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

and Applied Analysis 3 Proof. First we show thatN ̸ = 0. From (15) and (16), we rewrite J (φ, ψ) = 1 2 ( 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2) + 1 2 ( 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2) − 1 4 ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n ) , (18) I (φ, ψ) = 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2 + 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2 − ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n )...

Abstract The aim of this article is to introduce α \alpha - ψ \psi -proximal contraction in the setting ℱ -metric space and prove existence best proximity points for these contractions. As applications our main results, we obtain coupled on equipped with an arbitrary binary relation.

A new mixed variational–hemivariational problem is introduced, a(u,v−u)+b(v−u,λ)+φ(v)−φ(u)+J0(Tu;Tv−Tu)≥(f,v−u)X, b(u,μ−λ)−ψ(μ)+ψ(λ)−Ψ0(Rλ;Rμ−Rλ)≤0, (v∈X, μ∈Λ⊆Y), focusing on its well-posedness. We are looking for a pair solution (u,λ)∈X×Λ working into Hilbert spaces framework. Some particular cases with applications in mechanics highlighted. special attention payed to case leading penalty term...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.