Volume 46, Issue 4

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCI p of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI .

The aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.

The following version of the weighted Hermite–Hadamard inequalities for set-valued functions is presented: Let Y be a Banach space and F : [ a , b ] → cl ( Y ) be a continuous set-valued function. If F is convex, then F(xμ)⊃1μ([a,b])∫abF(x) dμ(x)⊃b−xμb−aF(a)+xμ−ab−aF(b),$$F(x_\mu ) \supset {1 \over {\mu ([a,b])}}\int\limits_a^b {F(x)\;d\mu (x) \supset {{b - x_\mu } \over {b - a}}} F(a) + {{x_\mu - a} \over {b - a}}F(b),$$ where μ is a Borel measure on [ a , b ] and x μ is the barycenter of μ on [ a , b ]. The converse result is also given.

In the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.

We review properties of the q -Hermite polynomials and indicate their links with the Chebyshev, Rogers–Szegö, Al-Salam–Chihara, continuous q -utraspherical polynomials. In particular, we recall the connection coefficients between these families of polynomials. We also present some useful and important finite and infinite expansions involving polynomials of these families including symmetric and non-symmetric kernels. In the paper, we collect scattered throughout literature useful but not widely known facts concerning these polynomials. It is based on 43 positions of predominantly recent literature.

In this paper we give some new results on complete abstract second order differential equations of elliptic type set in ℝ + . In the framework of UMD spaces, we use the celebrated Dore–Venni Theorem to prove existence and uniqueness for the strict solution. We will use also the Da Prato–Grisvard Sum Theory to furnish results when the space is not supposed to be a UMD space.

In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators T λ f of the form (Tλ f) (x)=∫abKλ(t−x, f(t)) dt,      x∈ (a, b),$$(T_\lambda \,f)\,(x) = \int\limits_{\rm{a}}^{\rm{b}} {K_\lambda (t - x,\,f(t))\,dt,\,\,\,\,\,\,x \in \,(a,\,b),} $$ acting on functions with bounded (Jordan) variation on an interval [ a , b ], as λ → λ 0 . Here, the kernels 𝕂 = { K λ } λ ∈Λ satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].

In this paper, we extend the notion of essential range to vector-valued functions and present various equivalent conditions for the injectiveness of the composition operators alongwith a characterisation for measurable transformations inducing composition operators between Lorentz–Bochner spaces. Some aspects of the weighted composition operators on Lorentz–Bochner spaces, induced by a measurable transformation and an operator valued map, are also discussed.

The purpose of this paper is to prove common fixed point theorems for a family of mappings in symmetric spaces using the property (E.A) and weak compatibility or occasionally weak compatibility. Our results extend some recent results.

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicit iteration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

G. Chen [1] developed Chinese checker metric for the plane on the question “how to develop a metric which would be similar to the movement made by playing Chinese checker” by E. F. Krause [13]. Tian [17] developed α -metric which is defined by dα(P1,P2)=max{|x1-x2|,|y1-y2|}+(secα-tanα) min{|x1-x2|,|y1-y2|}$$d_\alpha (P_1 ,P_2 ) = \max \{ \left| {x_1 - x_2 } \right|,\left| {y_1 - y_2 } \right|\} + (\sec \alpha - \tan \alpha )\;\min \{ \left| {x_1 - x_2 } \right|,\left| {y_1 - y_2 } \right|\} $$ where P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) are two points in analytical plane, and α ∈ [0, π/4] : Stewart’s theorem yields a relation between lengths of the sides of a triangle and the length of a cevian of the triangle. A taxicab and Chinese checkers analogues of Stewart’s theorem are given in [12] and [9], respectively. In this work, we give an α -analog of the theorem of Stewart by using the base line concept and we give a α -analog of formulae for the medians which is the application of Stewart’s theorem.