Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K X be a nonself mapping, satisfying Condition (E) with F(T): = {x K : Tx = x} ≠ ∅. Suppose {x n } is generated iteratively by x 1 K, x n+1 = P ((1 -a n )x n ⊕ a n TP [(1 -b n )x n ⊕ b n Tx n ]),n ≥ 1, where {a n } and {b n } are real sequences in [ε, 1 -ε] for some ε (0, 1). Then, {x n } Δ-converges to some point x ⋆ in F(T). This extends a result of Laowang and Panyanak [Fixed Point Theory Appl. 367274, 11 (2010)] for nonself mappings satisfying Condition (E).

In current research, the optimization of ohmic heating on greater lizardfish ( Saurida tumbil) sausage variables was carried out using response surface methodology-central composite design (RSM-CCD). The effect of process variables including voltage gradient (15–60 V/cm), time (1–15 min), and temperature (60–90°C) on the microbial properties, pH, peroxide value, water holding capacity (WHC), and cooking loss of the sausages was evaluated. The results showed that the characteristics of the sausages were dependent on the ohmic heating conditions and these properties can be modulated. As per the results, the voltage gradient and temperature has a significant effect on the total plate count (p < 0.05). The increase in voltage gradient was the most effective on pH (5.63–6.91). The interaction terms of all items had a significant effect (p < 0.05) on the peroxide value of the fish sausages. Higher amount of temperature and process time were resulted in the more cooking loss. Increasing the voltage gradient was more effective on WHC compared to the temperature. Finally, the process was optimized and the optimized condition was achieved by setting the voltage gradient at 30 V/cm, process time at 4 min, and temperature at 66°C. Also, it was compared with conventional heating. The results were shown that the differences between the mean values of all responses were statistically significant (p < 0.05) except for pH. Therefore, ohmic method was carried out faster, with lower temperature and obtaining the highest WHC and lowest total plate count, peroxide value, cooking loss, and optimized pH. Generally, this study suggested that the ohmic heating can be used as a rapid and homogeneous cooking method for the preparation of sausages from greater lizardfish as a commercial low-valued fish.

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In this paper, the existence of solutions of some minimization problems for noncyclic mappings in G metric spaces is studied. Our results can be considered as an extension of Abkar and Gabeleh's result [Global Optimal Solutions of Noncyclic Mappings in Metric Spaces, J. Optim. Theory. Appl. 153 (2011), 298-305] to the case of G metric spaces.