Keywords: Hurwitz–Lerch Zeta function Lipschitz–Lerch Zeta function Lerch Zeta function Hurwitz Zeta function Riemann Zeta function Legendre chi function Bernoulli polynomials Bernoulli numbers Discrete Fourier transform a b s t r a c t It is shown that there exists a companion formula to Srivastava's formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bern...

We show that the analytic continuations of Helson zeta functions ζ χ ( s ) = ∑ 1 ∞ n − $ \zeta _\chi (s)= \sum _1^{\infty }\chi (n)n^{-s}$ can have essentially arbitrary poles and zeroes in strip 21 / 40 < ℜ 21/40 \Re 1$ (unconditionally), whole critical 2 1/2 <1$ under Riemann Hypothesis, with function \chi$ taking values cubic roots unity. If sets are symmetric respect to real axis, same be a...

in this paper,  we introduce the notion of  generalized multivalued  $f$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  our results extend and improve the results announced by many others with less hypothesis. also, we give some illustrative examples.

Two genes for ornithinetranscarbamylase exist in strain Escherichia coli K-12, argI, at 85 min, and argF, at 7 min. In an attempt to compare the deoxyribonucleic acid material of these two genes, the lambda transducing phages carrying a portion of the argI region, lambda dvalS argI, lambda pvalS, and lambda dvalS pyrB, and of the argF region, lambda dargF, have been isolated. Their structure, i...

The main objective of this work is to introduce a new type non-linear contraction via C-class functions by using ?-admissible mapping. Our results extend and generalize the very recent Karapinar Sadarangani (2015. RACSAM. [37]). Illustrative examples are given support our findings. We have shown that satisfy periodic fixed point after modifying contraction. Next, we findings from self-mapping T...

Gender differences in vascular reactivity have been suggested; however, the cellular mechanisms involved are unclear. We tested the hypothesis that the gender differences in vascular reactivity reflect gender-related, possibly estrogen-mediated, distinctions in the expression and activity of specific protein kinase C (PKC) isoforms in vascular smooth muscle. Aortic strips were isolated from int...

In this work, we give a partial positive answer to the question concerning set-valued quasicontraction proposed by Amini-Harandi (Appl. Math. Lett. 24:1791-1794 2011). By useful lemma, prove fixed point theorem for quasi-contraction, which extends range of contraction constant in result from [0, 1/2) 1/3? 3). Also, new simple proof quasi-contraction type Haghi et al. 25:843-846 2012). Finally, ...

In this paper, we prove a fixed point theorem for the sum of a nonlinear contraction mapping and compact operator. The fixed point theorem obtained here resembles that of Krasnoselskii in which the mapping function is a combination of contraction and compact operators. It also takes the form of Schaefer’s fixed point theorem of continuation type. Criteria on periodicity and control in integral ...

In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inco...

in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.