The aim of the present paper is to obtain a number of Kuhn-Tucker type sufficient optimality conditions for a feasible solution to be an efficient solution under the assumptions of the new notions of weak strictly pseudo quasi α-univex, strong pseudo quasi α-univex, and weak strictly pseudo α-univex vector valued functions. We also derive the duality theorems for Mond-Weir and general Mond-Wei...

Let K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemicontractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, conv...

The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim\_{\theta}\Lambda$, interpolate between its Hausdorff and box using the parameter $\theta\in\[0,1]$. For Bedford–McMullen carpet $\Lambda$ with distinct dimensions, we show that $\dim\_{\theta}\Lambda$ is strictly less than dimension for every $\theta<1$. Moreover, derivative upper bound positive at $\theta=1$. This answe...

Light Affine Lambda Calculus is a term calculus for polynomial time computation ([12]). Some of the terms of Light Affine Lambda Calculus must however be regarded as errors. Intuitionistic Light Affine Logic (ILAL) types only terms without errors, but not all of them. We introduce two type assignment systems with intersection types : in the first one, typable pseudo-terms are exactly the terms ...

We demonstrate that in the context of statically typed pure functional lambda calculi, exceptions are strictly more powerful than call/cc. More precisely, we prove that the simply typed lambda calculus extended with exceptions is strictly more powerful than Girard's F ! [6, 15] (a superset of the simply typed lambda calculus) extended with call/cc and abort. This result is established by showin...

and Applied Analysis 3 Lemma 7 (see [15]). LetC be a nonempty closed convex subset of a real Hilbert space H. Let T : C 󳨃→ C be a k-strict pseudo-contractive mapping. Let γ and δ be two nonnegative real numbers such that (γ + δ)k ≤ γ; then 󵄩󵄩󵄩γ (x − y) + δ (Tx − Ty) 󵄩󵄩󵄩 ≤ (γ + δ) 󵄩󵄩󵄩x − y 󵄩󵄩󵄩 , ∀x, y ∈ C. (21) Lemma 8 (see [16]). Let H be a Hilbert space and C a nonempty convex subset of H. Let...