In this paper, we express and prove Chebyshev weighted type inequality for fuzzy integrals and in abstract spaces where the functions are strictly monotone functions. Furthermore, we have shown our results for n-th strictly monotone functions. The theorems are illustrated with several examples.

Let p ³ 1 and ( Wn) n w be a sequence with non-negative entries. If (tn,k) ³0, denote by ||T||p,x the infimum of those U satisfying the following inequality:(S¥n=1wn(S¥k=1 tn,k ak)p)1/p £U (S¥k=1 WKAPK)1/P ,whenever ( an) ∈lp (w ) n p a ∈l w . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,¥). We considered this problem for certain matrix operators such as Norlund, weighted mean, Ceasaro and Copson matrices. This problem is considered by some authors like Bennett, Jamson and the first author on sequence spaces lp and weighted sequence spaces for some kind of matrix operators. Also, this study is an extension of paper by Chang-Pao Chen, Dah-Chin Luor and Zong-Yin Ou.

In this paper, we use the $(k, \psi)$-Hilfer fractional integral of functions with respect to another function to generalize Chebyshev-type fractional integral inequalities. Some inequalities involving $(k, \psi)$-Hilfer fractional integrals are also to be proved.

For 0 < r < 1 and 1£ p£q < ¥ we find necessary and sufficient conditions for the validity of the following inequality: (òba u(x) (òxa | g(x)-g (t)| r w(t)dt)q/r dx)1/q £ c(òba v(x)| g’ (x)|p dx)1/pwhere u(·), v(·), and w(·) are weight functions.

We establish the Brunn-Minkowski-type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies.

Please click on PDF to view the abstract

weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operators, composition operators, multiplication operators and composition operators followed by differentiation operators. In this paper we study generalized weighted composition operators and give estimates for the essential norm of such operators on certain Banach spaces of analytic functions into weighted type spaces. The underlying Banach spaces of analytic functions include Bloch spaces, Zygmund spaces and weighted type spaces. Our estimates for the essential norms of generalized weighted composition operators imply necessary and sufficient conditions for the compactness of such operators. As another application of our results, we obtain essential norm estimates of certain well-known operators which are special cases of generalized weighted composition operators.